Longitudinal Quantile Regression and its Application in Medical Research

Longitudinal Quantile Regression and its Application in Medical Research

Quantile regression is an Evolving body of statistical methods for Estimating and drawing inferences about conditional quantile functions. However inference for these models is challenging, particularly for clustered data. This paper investigates a class of pernalized quantile regression Estimators for longitudinal data. The penalized least squares interpretation of the classical random effects Estimator suggests a possible way forward for quantile regression models with a large number of fixed effects. The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. Å general approach to Estimating quantile regression models for longitudinal data is represented employing £1 regularization methods. Sparse linear algebra, and interior point methods for solving large linear programs are essential computational tools. An application of the proposed method was illustrated for analyzing a longitudinal data of growth development in early treated children with congenital hypothyroidism.